A145543 Denominators in continued fraction expansion of sqrt(3/5).
1, 4, 9, 31, 71, 244, 559, 1921, 4401, 15124, 34649, 119071, 272791, 937444, 2147679, 7380481, 16908641, 58106404, 133121449, 457470751, 1048062951, 3601659604, 8251382159, 28355806081, 64962994321, 223244789044, 511452572409, 1757602506271, 4026657584951
Offset: 1
Examples
Since the partial quotients of CF sqrt(3/5)= [1, 3, 2, 3, 2, 3,...] denominators are 1, 4, 9, 31, 71, 244, 559,...; given a(1) = 1, a(2) = 4.
Crossrefs
Cf. A145542.
Programs
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Mathematica
Rest @ Denominator @ Convergents [Sqrt[3/5], 30] (* Amiram Eldar, Feb 26 2020 *)
Formula
Use the partial quotients of the continued fraction expansion of sqrt(3/5) as recursive operation multipliers, given a(1) = 1, a(2) = 4.
Empirical G.f.: x*(1+4*x+x^2-x^3)/(1-8*x^2+x^4). - Colin Barker, Jan 04 2012
Extensions
More terms from Amiram Eldar, Feb 26 2020
Comments